Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19153839 | C2 | semidirect |
| 2. C2×D8×D181 | C2 | semidirect |
| 3. #26041922 | C2 | semidirect |
| 4. #26041517 | C2 | semidirect |
| 5. #26041512 | C2 | semidirect |
| 6. #26041491 | C2 | semidirect |
| 7. #26041428 | C2 | semidirect |
| 8. #26041423 | C2 | semidirect |
| 9. C4×D1448 | C2 | semidirect |
| 10. C8×D724 | C2 | semidirect |
| 11. #495×C181 | C2 | semidirect |
| 12. C2×#15668450 | C22 | semidirect |
| 15. C2×#15668436 | C22 | semidirect |
| 20. C2×C8×D181 | C22 | semidirect |
| 24. #19153787 | C22 | semidirect |
| 27. C4×D724 | C22 | semidirect |
| 29. #19153750 | C22 | semidirect |
| 30. C4⋊#13089678 | C22 | semidirect |
| 31. #19153740 | C22 | semidirect |
| 32. #19153738 | C22 | semidirect |
| 33. #19153737 | C22 | semidirect |
| 35. #19153728 | C22 | semidirect |
| 36. C2×Q16×C181 | C22 | semidirect |
| 37. C2×SD16×C181 | C22 | semidirect |
| 39. #124×C181 | C22 | semidirect |
| 40. C4×C8×C181 | C22 | semidirect |
| 56. D1448 | D4 | semidirect |
| 127. C2×D181 | #135 | semidirect |
| 143. C181 | #3280 | semidirect |
| 148. #495 | D181 | semidirect |
| 159. C2×Q16 | C2×D181 | semidirect |
| 161. C2×SD16 | C2×D181 | semidirect |
| 168. #124 | C2×D181 | semidirect |
| 184. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×D8×D181 | 2 |
| #26041922 | 2 |
| #26041517 | 2 |
| #26041512 | 2 |
| #26041491 | 2 |
| #26041428 | 2 |
| #26041423 | 2 |
| C4×D1448 | 2 |
| C8×D724 | 2 |
| #495×C181 | 2 |
| #3280 | 181 |